Tran Wheeler
01/20/2023 · Senior High School
The Coffee Counter charges \( \$ 9 \) per pound for Kenyan French Roast coffee and \( \$ 8 \) per pound for Sumatran coffee. How much of each type should be used to make a 20 pound blend that sells for \( \$ 8.70 \) per pound? The Coffee Counter should mix \( \square \) pounds of Kenyan Roast coffee and \( \square \) pounds of Sumatran coffee to make 20 pounds of a blend that sells for \( \$ 8.70 \) per pound.
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Let \( x \) be the number of pounds of Kenyan French Roast coffee, and \( y \) be the number of pounds of Sumatran coffee. We have the following system of equations based on the problem statement:
1. The total weight of the blend:
\[
x + y = 20
\]
2. The total cost of the blend:
The cost of the blend should equal the selling price per pound multiplied by the total weight:
\[
9x + 8y = 8.70 \times 20
\]
Calculating the right side of the second equation:
\[
8.70 \times 20 = 174
\]
So, the second equation becomes:
\[
9x + 8y = 174
\]
Now we have the system of equations:
1. \( x + y = 20 \)
2. \( 9x + 8y = 174 \)
We can solve this system using substitution or elimination. Let's use substitution. From the first equation, we can express \( y \) in terms of \( x \):
\[
y = 20 - x
\]
Now, substitute \( y \) into the second equation:
\[
9x + 8(20 - x) = 174
\]
Expanding this gives:
\[
9x + 160 - 8x = 174
\]
Combining like terms:
\[
x + 160 = 174
\]
Subtracting 160 from both sides:
\[
x = 14
\]
Now, substitute \( x = 14 \) back into the equation for \( y \):
\[
y = 20 - 14 = 6
\]
Thus, the Coffee Counter should mix:
- \( 14 \) pounds of Kenyan French Roast coffee
- \( 6 \) pounds of Sumatran coffee
In conclusion, the Coffee Counter should mix \( \boxed{14} \) pounds of Kenyan Roast coffee and \( \boxed{6} \) pounds of Sumatran coffee to make a 20-pound blend that sells for \( \$ 8.70 \) per pound.
Quick Answer
Mix 14 pounds of Kenyan Roast and 6 pounds of Sumatran coffee.
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